Generally, image and video compression involves the application of data compression on digital images (either individual stand alone images or images that are part of image sequences in a video). Image compression may be used as a general term to apply to both image compression and video compression. An objective of image compression is to reduce redundancy present in image data in order to store and/or transmit images in an efficient form.
Joint Photographic Expert Group (JPEG) defined an image compression method that has become a technical standard and is widely used for compressing digital images. JPEG compression utilizes lossy compression, meaning that some visual quality is lost in the compression process and cannot be restored. Standard JPEG decompression reconstructs quantized discrete cosine transform (DCT) coefficients to a center of a quantization bin. This may fail to exploit a non-uniform distribution of AC coefficients. Commonly used dequantization techniques assume a Laplacian distribution instead of a uniform distribution, which can achieve 0.25 dB using a maximum likelihood (ML) estimate.
In work by E. Candes, et. al., entitled “Quantitative Robust Uncertainty Principles and Optimally Sparse Decomposition,” IEEE Transactions on Information Theory, 52(2), pp. 489-509, February 2006 and by D. Donoho, entitled “Compressive Sensing,” IEEE Transactions on Information Theorgy, 52(4), pp. 1289-1306, April 2006, compressive sensing (CS) theory is presented. They demonstrate that information contained in a few significant coefficients may be captured by a small number of random linear projections. An original signal may then be reconstructed from the random linear projections using an appropriate decoding scheme. Furthermore, the two references have shown that it is possible to reconstruct a compressive signal by solving a convex optimization problem.